Ukraine’s new Western-backed president has declared a week-long unilateral ceasefire and unveiled a sweeping plan for curbing a pro-Russian insurgency that killed 13 more soldiers in fierce clashes in the eastern rustbelt.

But both the Kremlin and a senior rebel commander immediately rejected Petro Poroshenko’s proposals for ending the battles that have claimed the lives of more than 375 people and left the ex-Soviet country on the verge of splitting in two.

US President Barack Obama, French counterpart Francois Hollande and German Chancellor Angela Merkel welcomed the unilateral ceasefire announcement while warning of further possible steps to “impose costs on Russia” if Moscow fails to de-escalate the situation, the White House said.

Obama spoke separately with Merkel and Hollande on Friday and the three leaders stressed the need for Russia to pull back its “destabilising presence” from the border, a White House official added.

The Kremlin swiftly dismissed the ceasefire as “not an invitation to peace and negotiations but an ultimatum for the militias in the southeast of Ukraine to give up their weapons”. Valeriy Bolotov of the self-proclaimed Lugansk People’s Republic warned that “no one will lay down their arms until there is a full troop withdrawal from our land”.

And Poroshenko himself stressed on his first visit to the restive Russian-border region since assuming office on June 7 that the order for Ukrainian soldiers to halt fire “does not mean that we will not fight back against aggression toward our troops.” A Ukranian security spokesman reported that the latest battles had claimed the lives of 13 soldiers – a toll underscoring the uptick in violence witnessed in the past week.

Kiev was also forced to fend off Moscow’s charges that Ukrainian forces had wounded a Russian border official when a shell crossed the border during a recent clash. The Kremlin demanded “an explanation and an apology”.

Ukraine’s defence ministry said the rocket grenade had been fired by pro-Russian “bandits” and denied its soldiers’ involvement. The sense that tensions on the ground were rising was further reinforced when Washington followed up similar charges from NATO by accusing the Kremlin of stirring up new trouble along its western neighbour’s frontier.

A senior US administration official said Russia had deployed “significant” military forces near Ukraine “to provide active support for separatist fighters”.